The problem of estimating, under unweighted quadratic loss, the mean of a multinormal random vector X with arbitrary covariance matrix V is considered. The results of James and Stein for the case V = I have since been extended by Bock to cover arbitrary V and also to allow for contracting X...

An apparent gap in the proof of Creasy's t test is filled and some false statements on this topic, found in the literature, are corrected. Creasy's test is shown to be identical with Williams' t test. The latter can be generalized to the multivariate case of a linear functional relationship.

The authors investigated the asymptotic joint distributions of certain functions of the eigenvalues of the sample covariance matrix, correlation matrix, and canonical correlation matrix in nonnull situations when the population eigenvalues have multiplicities. These results are derived without...

We compare the merits of two orthogonal series methods of estimating a density and its derivatives on a compact interval--those based on Legendre polynomials, and on trigonometric functions. By examining the rates of convergence of their mean square errors we show that the Legendre polynomial...

Limit theorems are given for the eigenvalues of a sample covariance matrix when the dimension of the matrix as well as the sample size tend to infinity. The limit of the cumulative distribution function of the eigenvalues is determined by use of a method of moments. The proof is mainly...

Consider estimating a smooth p-variate density f at 0 using the classical kernel estimator fn(0) = n-1 [Sigma]ibn-pw(bn-1Xi) based on a sample {Xi} from f. Under familiar conditions, assigning bn = bn-1/(4 + p) gives the best MSE decay rate O(n-4/(4 + p), but the optimal b, b* say, depends on f...

The aim of the present paper is to obtain estimates of the speed of convergence in the central limit theorem in Rk for variation distance valid when (truncated) pseudo-moments are small enough. Together with the integral type estimates of Bhattacharya and Sweeting [5,6] the results of this paper...

Let (X, Y) have regression function m(x) = E(Y X = x), and let X have a marginal density f1(x). We consider two nonparameteric estimates of m(x): the Watson estimate when f1 is known and the Yang estimate when f1 is known or unknown. For both estimates the asymptotic distribution of the maximal...

If X1,...,Xn are independent identically distributed Rd-valued random vectors with probability measure [mu] and empirical probability measure [mu]n, and if is a subset of the Borel sets on Rd, then we show that P{supA[set membership, variant][mu]n(A)-[mu](A)=[var epsilon]} = cs(, n2)e-2n[set...

This article attempts to lay a proper foundation for studying asymptotic properties of nonhomogeneous diffusions, extends earlier criteria for transience, recurrence, and positive recurrence, and provides sufficient conditions for the weak convergence of a shifted nonhomogeneous diffusion to a...